Adaptive control of uncertain pure-feedback nonlinear systems

An adaptive control approach is proposed to solve the globally asymptotic state stabilisation problem for uncertain pure-feedback nonlinear systems which can be transformed into the pseudo-affine form. The pseudo-affine pure-feedback nonlinear system under consideration is with nonlinearly parameterised uncertainties and possibly unknown control coefficients. Based on the parameter separation technique, a novel backstepping controller is designed by adopting the adaptive high gain idea. The proposed control approach could avoid the drawbacks of the approximation-based approaches since no estimators are needed to estimate the virtual and the actual controllers. In addition, it could guarantee globally asymptotic state stabilisation even though there exist nonlinearly parameterised uncertainties in the considered system while comparing to the existing approximation-free approaches. A numerical and a realistic examples are employed to demonstrate the effectiveness of the proposed control method.     

Robust global stabilization of linear systems with input saturation via gain scheduling

The problem of robust global stabilization of linear systems subject to input saturation and input‐additive uncertainties is revisited in this paper. By taking advantages of the recently developed parametric Lyapunov equation‐based low gain feedback design method and an existing dynamic gain scheduling technique, a new gain scheduling controller is proposed to solve the problem. In comparison with the existing ?₂‐type gain scheduling controller, which requires the online solution of a state‐dependent nonlinear optimization problem and a state‐dependent ?₂ algebraic Riccati equation (ARE), all the parameters in the proposed controller are determined a priori. In the absence of the input‐additive uncertainties, the proposed controller also partially recovers Teel's ?_∞‐type scheduling approach by solving the problem of global stabilization of linear systems with actuator saturation. The ?_∞‐type scheduling approach achieves robustness not only with non‐input‐additive uncertainties but also requires the closed‐form solution to an ?_∞ ARE. Thus, the proposed scheduling method also addresses the implementation issues of the ?_∞‐type scheduling approach in the absence of non‐input‐additive uncertainties. Copyright © 2009 John Wiley & Sons, Ltd.     

Stabilisation of controlled positive delayed continuous-time systems

This article solves the stabilisation problem by output feedback control for linear continuous-time systems with delay. This technique can be applied for both positive systems and controlled positive systems (systems becoming positive in closed-loop). The synthesis of feedback controllers is solved in terms of linear programs, extending the solution also to stabilisation with bounded control and stabilisation by controllers with the memory of the delayed state. The proposed conditions do not involve the value of the delay. Some examples illustrate the proposed approach.     

Event-triggered control for semi-global stabilisation of systems with actuator saturation

This paper investigates the problem of event-triggered control for semi-global stabilisation of null controllable systems subject to actuator saturation. First, for a continuous-time system, novel event-triggered low-gain control algorithms based on Riccati equations are proposed to achieve semi-global stabilisation. The algebraic Riccati equation with a low-gain parameter is utilised to design both the event-triggering condition and the linear controller; a minimum inter-event time based on the Riccati ordinary differential equation is set a priori to exclude the Zeno behaviour. In addition, the high–low gain techniques are utilised to extend the semi-global results to event-based global stabilisation. Furthermore, for a discrete-time system, novel low-gain and high–low-gain control algorithms are proposed to achieve event-triggered stabilisation. Numerical examples are provided to illustrate the theoretical results.     

Delay-dependent stability and stabilisation of continuous 2D delayed systems with saturating control

This paper deals with the stabilisation problem of continuous two-dimensional (2D) delayed systems, in the presence of saturations on the control signals. For this, a new delay decomposition approach is proposed to deal with the stability and stabilisation issues. The idea is that the range of variation of each delay is divided into segments, and a specific Lyapunov– Krasovskii functional is used that contains different weight matrices in each segment. Then, based on this approach, new delay-dependent stability and stabilisation criteria for continuous 2D delayed systems are derived. These criteria are less conservative and include some existing results as special cases. Some numerical examples are provided to show that a significant improvement is achieved using the proposed approach.     

Robust decentralised observer based guaranteed cost control for nonlinear uncertain interconnected systems. Application to multi-machine power systems

This article addresses the problem of a robust decentralised observer based guaranteed cost control for nonlinear interconnected systems with norm bounded time varying parameter uncertainties.

Sufficient conditions for the robust stabilisation and the guaranteed cost control performances of the closed-loop system are formulated in an optimisation problem in terms of linear matrix inequalities. Moreover, the designed problem is solved by a proposed iterative algorithm to compute the observer and the control gain matrices, to minimise the upper bound of a prescribed performance index and to maximise the nonlinearity domain, which leave the augmented system stable, despite the emerged uncertainties on the subsystems and on the interconnections between them. An extensive application example of a power system with three interconnected machines is discussed to demonstrate the reliability of the proposed control approach.     

Stabilisation analysis for switched neutral systems based on sampled-data control

In this paper, the problem of stabilisation analysis for switched neutral systems based on sampled-data control and average dwell time approach is investigated. Delay-dependent stabilisation results are derived in terms of linear matrix inequalities by constructing piecewise Lyapunov–Krasovskii functional based on the Wirtinger's inequality. Also, the controller gain matrix is designed by applying an input-delay approach. Further convex combination technique and some integral inequalities are used to derive less conservative results. The effectiveness of the derived results is validated through numerical examples.     

Global adaptive exponential stabilisation for nonlinear systems with multiple unknown control directions

In this paper, we address the global generalised exponential stabilisation problem for a class of lower-triangular systems with multiple unknown directions. Instead of the well-known Nussbaum-gain adaptive rule, a Lyapunov-based adaptive logic switching rule is proposed to seek the correct control directions for such systems. The main advantage of the proposed controller is that it can guarantee the global generalised exponential stability of closed-loop systems. Simulation examples are given to verify the effectiveness of the developed control approach.     

Universal stabilisation design for uncertain nonlinear system with sign-switching unknown control direction

A universal robust control approach is proposed to stabilise a class of nonlinear systems. The system contains both nonlinear dynamics uncertainty and an unknown control direction, which is the multiplier of the control term. Being different from most previous studies, the unknown control direction is allowed to switch its sign in this article. A new Nussbaum gain technique is designed and integrated with robust controller to tackle the sign-switching unknown control direction. It is proven that the proposed control approach can yield asymptotic stabilisation and guarantee the boundedness of the closed-loop signals. In addition, these results can be readily extended to tracking problems under a different assumption.     

Controller synthesis for switched positive linear systems by output feedback

The output-feedback controller synthesis issue for a class of continuous-time switched linear systems via average dwell time switching with constrained controls and output is addressed. First, we focus on the output-feedback stabilisation by decomposing control gain matrix. Second, the stabilisation problem with sign-restricted controls while imposing positivity and stability on closed-loop system is solved, then the results extend to asymmetrically bounded controls and constrained outputs. All the derived conditions are formulated as linear programming. Finally, numerical examples are given to show the applicability of the proposed methods.     

Robust reliable sampled-data control for switched systems with application to flight control

This paper addresses the robust reliable stabilisation problem for a class of uncertain switched systems with random delays and norm bounded uncertainties. The main aim of this paper is to obtain the reliable robust sampled-data control design which involves random time delay with an appropriate gain control matrix for achieving the robust exponential stabilisation for uncertain switched system against actuator failures. In particular, the involved delays are assumed to be randomly time-varying which obeys certain mutually uncorrelated Bernoulli distributed white noise sequences. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and employing an average-dwell time approach, a new set of criteria is derived for ensuring the robust exponential stability of the closed-loop switched system. More precisely, the Schur complement and Jensen's integral inequality are used in derivation of stabilisation criteria. By considering the relationship among the random time-varying delay and its lower and upper bounds, a new set of sufficient condition is established for the existence of reliable robust sampled-data control in terms of solution to linear matrix inequalities (LMIs). Finally, an illustrative example based on the F-18 aircraft model is provided to show the effectiveness of the proposed design procedures.     

The active disturbance rejection control approach to stabilisation of coupled heat and ODE system subject to boundary control matched disturbance

We consider stabilisation for a linear ordinary differential equation system with input dynamics governed by a heat equation, subject to boundary control matched disturbance. The active disturbance rejection control approach is applied to estimate, in real time, the disturbance with both constant high gain and time-varying high gain. The disturbance is cancelled in the feedback loop. The closed-loop systems with constant high gain and time-varying high gain are shown, respectively, to be practically stable and asymptotically stable.     

Cooperative output regulation of heterogeneous multi-agent systems based on passivity

This paper investigates the problem of cooperative output regulation of heterogeneous linear multi-agent systems. A passive framework is presented for the stabilisation analysis of cooperative output regulation, which can overcome the difficulty caused by the fact that the global dynamics of heterogeneous multi-agent systems depends on the global communication structure. An adaptive distributed observer is proposed to estimate the state of the exosystem, and the proposed distributed observer is independent of any global information of the communication graph. Based on passivity design and adaptive distributed observer, both a distributed state feedback and a distributed output feedback protocol are designed for output synchronisation of heterogeneous multi-agent systems. The gain matrices of the distributed protocols and observers are obtained by a Riccati equation design approach. Furthermore, sufficient local conditions for solving the problem of cooperative output regulation of heterogeneous multi-agent systems are presented. Finally, numerical simulation results are given to illustrate the effectiveness of the proposed distributed control schemes.     

Hybrid fuzzy control of robotics systems

This paper presents a new approach towards optimal design of a hybrid fuzzy controller for robotics systems. The salient feature of the proposed approach is that it combines the fuzzy gain scheduling method and a fuzzy proportional-integral-derivative (PID) controller to solve the nonlinear control problem. The resultant fuzzy rule base of the proposed controller can be decomposed into two layers. In the upper layer, the gain scheduling method is incorporated with a Takagi-Sugeno (TS) fuzzy logic controller to linearize the robotics system for a given reference trajectory. In the lower layer, a fuzzy PID controller is derived for all the locally linearized systems by replacing the conventional PI controller by a linear fuzzy logic controller, which has different gains for different linearization conditions. Within the guaranteed stability region, the controller gains can be optimally tuned by genetic algorithms. Simulation studies on a pole balancing robot and a multilink robot manipulator demonstrate the effectiveness and robustness of the proposed approach.     

基于回路成形的鲁棒增益调度控制器设计

针对目前基于线性变参数系统的增益调度控制设计中存在的控制结构复杂性问题，提出一种基于回路成形的简单且易实现的增益调度控制结构.在此基础上，提出一个鲁棒增益调度控制设计方法.设计过程首先采用补偿器函数使得被控对象奇异值具有期望的形状，以保证被控对象的性能要求，然后利用小增益定理设计一个鲁棒控制器，得到具有良好性能的、结构简单的鲁棒增益调度控制器.最后针对一个化工过程，说明此方法的有效性.     

中立时滞LPV系统基于观测器的控制器设计

研究一类中立时滞线性参数变化系统的基于观测器的控制问题．呆用Lyapunov方法,提出了系统的时滞相关稳定性条件,设计了增益调度控制器和状态观测器．利用参数线性矩阵不等式,将控制器存在的充分条件转化为凸优化问题．最后通过数值仿真验证了所提出方法的可行性．     

An advanced fuzzy logic gain scheduling trajectory control for nonlinear systems

This paper investigates a novel fuzzy control approach developed for a class of nonlinear continuous systems. We combine an input–output feedback linearization (IOFL) method and a gain scheduling (GS) approach to obtain a tracking control structure. The latter is mainly based on the reversing trajectory method which allows us to estimate the asymptotic stability region around operating points. Needless to say that the limitation of this analytical approach lies in the challenge of determining the intermediate operating points in order to ensure a smooth transition from actual operating conditions to desired ones. This happens when there is no intersection between successive stability regions. The proposed fuzzy logic controller (FLC) is synthesized in order to determine the intermediate operating points which, in turn, will allows us to online implement the tracking control for nonlinear systems. Finally, the effectiveness of the fuzzy gain scheduling schema is demonstrated through its simulation to a temperature control problem in a CSTR.     

Control of discrete time nonlinear systems with a time-varying structure

In this paper, we present a control methodology for a class of discrete time nonlinear systems that depend on a possibly exogenous scheduling variable. This class of systems consists of an interpolation of nonlinear dynamic equations in strict feedback form, and it may represent systems with a time-varying nonlinear structure. Moreover, this class of systems is able to represent some cases of gain scheduling control, Takagi-Sugeno fuzzy systems, as well as input-output realizations of nonlinear systems which are approximated via localized linearizations. We present two control theorems, one using what we call a “global” approach (akin to traditional backstepping), and a “local” approach, our main result, where backstepping is again used but the control law is an interpolation of local control terms. An aircraft wing rock regulation problem with varying angle of attack is used to illustrate and compare the two approaches.     

Finite-time stabilisation for high-order nonlinear systems with low-order and high-order nonlinearities

This paper considers the finite-time stabilisation for a class of high-order nonlinear systems with both low-order and high-order nonlinearities. Based on the finite-time Lyapunov stability theorem together with the methods of dynamic gain control and adding one power integrator, a state feedback controller with gains being tuned online by two dynamic equations is proposed to guarantee the global finite-time stabilisation of the closed-loop system.     

Partial stabilisation of semilinear systems using bounded controls

This paper studies a partial stabilisation problem for distributed semilinear systems. This consists of steering only a part of the system’s state to its equilibrium. Constrained controls are proposed to force the desired part of the state to approach the equilibrium. Necessary and sufficient conditions for weak and strong partial stabilisation are given. Applications are presented.